Solve (m+3)^2(m-3)^2

$$( m + 3 ) ^ { 2 } ( m - 3 ) ^ { 2 }$$

Evaluate

$$\left(m^{2}-9\right)^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(m+3\right)^{2}.

$$\left(m^{2}+6m+9\right)\left(m-3\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(m-3\right)^{2}.

$$\left(m^{2}+6m+9\right)\left(m^{2}-6m+9\right)$$

Use the distributive property to multiply m^{2}+6m+9 by m^{2}-6m+9 and combine like terms.

$$m^{4}-18m^{2}+81$$

Expand

$$m^{4}-18m^{2}+81$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(m+3\right)^{2}.

$$\left(m^{2}+6m+9\right)\left(m-3\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(m-3\right)^{2}.

$$\left(m^{2}+6m+9\right)\left(m^{2}-6m+9\right)$$

Use the distributive property to multiply m^{2}+6m+9 by m^{2}-6m+9 and combine like terms.

$$m^{4}-18m^{2}+81$$